The United States said that the two days of talks in Doha were "serious and constructive" and that Washington, represented by CIA Director William Burns, offered ideas to close an agreement toward ending the 10-month conflict.
"This proposal builds on areas of agreement over the past week, and bridges remaining gaps in the manner that allows for a swift implementation of the deal," said a White House statement signed by co-mediators Qatar and Egypt.
"Senior officials from our governments will reconvene in Cairo before the end of next week with the aim to conclude the deal under the terms put forward today," it said.
Until the talks reconvene in Cairo, working-level teams will work out details including humanitarian provisions and practicalities for the release of hostages, it said. President Joe Biden called for the two-day talks in Doha in a rare joint statement last week with the leaders of Qatar and Egypt.
In that statement, Biden, President Abdel Fattah al-Sisi and Qatari Emir Sheikh Tamim bin Hamad Al-Thani said, "There is no further time to waste nor excuses from any party for further delay. It is time to release the hostages and detainees, begin the ceasefire, and implement this agreement."
Friday's statement said: "The path is now set for that outcome, saving lives, bringing relief to the people of Gaza, and de-escalating regional tensions."